MA 116 Turn-in Practice Problems 4.2 and 4.4 Pitts .docx
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MA 116 Turn-in Practice Problems 4.2 and 4.4
Pitts Name ___________________________
1. (4.4 # 4) The price p, in dollars, and the quantity x sold of a certain product obey the demand equation
1
100
3
p x
a.) Express the revenue R as a function of x. Show your work. ...
Slide Content
MA 116 Turn-in Practice Problems 4.2 and 4.4
Pitts Name ___________________________
1. (4.4 # 4) The price p, in dollars, and the quantity x sold of a
certain product obey the demand equation
1
100
3
a.) Express the revenue R as a function of x. Show your work.
c.) What is the revenue if 100 units are sold?
d.) What quantity x maximizes the revenue? What is the
maximum revenue? Show your
algebra. You may use
2
b
x
Pitts Name ___________________________
1. (4.4 # 4) The price p, in dollars, and the quantity x sold of a
certain product obey the demand equation
1
100
3
a.) Express the revenue R as a function of x. Show your work.
c.) What is the revenue if 100 units are sold?
d.) What quantity x maximizes the revenue? What is the
maximum revenue? Show your
algebra. You may use
2
b
x
a
Quantity x = ______________ Maximum revenue
______________
e.) What price should the company charge to maximize
revenue?
2. (4.4 # 6) The price p (in dollars) and the quantity x sold of a
certain product obey the demand equation
20 500 0 p 25
a.) Solve for p in terms of x. That is write p as a function of x.
b.) Express the revenue R as a function of x. Show your work
c.) What quantity x maximizes the revenue? What is the
maximum revenue? Show your algebra. Y
Quantity x = ______________ Maximum revenue
______________
e.) What price should the company charge to maximize
revenue?
2. (4.4 # 6) The price p (in dollars) and the quantity x sold of a
certain product obey the demand equation
20 500 0 p 25
a.) Solve for p in terms of x. That is write p as a function of x.
b.) Express the revenue R as a function of x. Show your work
c.) What quantity x maximizes the revenue? What is the
maximum revenue? Show your algebra. Y
Quantity x = ______________ Maximum revenue
______________
d.) What price should the company charge to maximize
revenue?
3. (4.4 # 8). Beth has 3000 feet of fencing to enclose a
rectangular field. (Show algebra)
a.) Express the area A of the rectangle as a function of x, where
x is the length of the rectangle.
b.) For what value of x is the area largest? Show algebra.
______________
d.) What price should the company charge to maximize
revenue?
3. (4.4 # 8). Beth has 3000 feet of fencing to enclose a
rectangular field. (Show algebra)
a.) Express the area A of the rectangle as a function of x, where
x is the length of the rectangle.
b.) For what value of x is the area largest? Show algebra.
c.) What is the maximum area?
3. (4.4 # 10). A farmer with 2000 meters of fencing wants to
enclose a rectangular plot that borders on a straight
highway, so he won’t fence the side along the highway.
Express the area A of the rectangle as a function of x.
highway
x
y
For what value of x is the area a maximum? Show algebra.
What is the maximum area?
5. (4.4 # 26). A shot-putter throws a ball at an inclination of
45o to the horizontal. The following data represents the
height of the ball h feet at the instant that it has traveled x feet
horizontally.
Distance x 20 40 60 80 100 120 140 160 180 200
3. (4.4 # 10). A farmer with 2000 meters of fencing wants to
enclose a rectangular plot that borders on a straight
highway, so he won’t fence the side along the highway.
Express the area A of the rectangle as a function of x.
highway
x
y
For what value of x is the area a maximum? Show algebra.
What is the maximum area?
5. (4.4 # 26). A shot-putter throws a ball at an inclination of
45o to the horizontal. The following data represents the
height of the ball h feet at the instant that it has traveled x feet
horizontally.
Distance x 20 40 60 80 100 120 140 160 180 200
Height h 25 40 55 65 71 77 77 75 71 64
b.) Using your graphing calcualtor find the quadratic function
of best fit that models the relation between
distance and height. Record your answer rounded to four
decimal places, but in your calculator store all the
decimals.
H(x) = _______________________________
c.) Use the function stored in your calculator to determine how
far the ball will travel before it reaches its
maximum height. Round to the nearest integer.
d.) What is that maximum height? Round to the nearest
integer.
6. See 4.2 # 22 c and g) A marketing firm wishes to find a
function that relates the sales S of a product and
A, the amount spent on advertising the product. The data are
obtained from past experience. Advertising
and sales are measure in thousands of dollars. Use your
graphing calculator; find the line of best fit relating
advertising expenditures and sales. Round to two decimal
b.) Using your graphing calcualtor find the quadratic function
of best fit that models the relation between
distance and height. Record your answer rounded to four
decimal places, but in your calculator store all the
decimals.
H(x) = _______________________________
c.) Use the function stored in your calculator to determine how
far the ball will travel before it reaches its
maximum height. Round to the nearest integer.
d.) What is that maximum height? Round to the nearest
integer.
6. See 4.2 # 22 c and g) A marketing firm wishes to find a
function that relates the sales S of a product and
A, the amount spent on advertising the product. The data are
obtained from past experience. Advertising
and sales are measure in thousands of dollars. Use your
graphing calculator; find the line of best fit relating
advertising expenditures and sales. Round to two decimal
places.
Advertising A 20 22 22.5 24 24 27 28.3
Sales, S 335 339 338 343 341 350 351
Equation: S = _______________________________ Round
to two decimal places.
g.) Predict sales if advertising expenditures are $25,000. Sales:
________________ Round to nearest integer
MA 116 Turn in Practice Problems (4.1 and 4.3)
Pitts Name ________________________________
1. (See 4.1 # 40) Suppose that the quantity supplied S and
quantity demanded D of hot dogs at a baseball game
are given by the following functions: S(p) = -2000 + 3000p
and D(p) = 10,000 – 1000p
where p is the price in dollars. The equilibrium price of a
market is defined as the price at which quantity
supplied equals quantity demanded (S = D). Show your work!!
a.) Find the equilibrium price for hot dogs at the baseball game.
What is the equilibrium quantity?
Advertising A 20 22 22.5 24 24 27 28.3
Sales, S 335 339 338 343 341 350 351
Equation: S = _______________________________ Round
to two decimal places.
g.) Predict sales if advertising expenditures are $25,000. Sales:
________________ Round to nearest integer
MA 116 Turn in Practice Problems (4.1 and 4.3)
Pitts Name ________________________________
1. (See 4.1 # 40) Suppose that the quantity supplied S and
quantity demanded D of hot dogs at a baseball game
are given by the following functions: S(p) = -2000 + 3000p
and D(p) = 10,000 – 1000p
where p is the price in dollars. The equilibrium price of a
market is defined as the price at which quantity
supplied equals quantity demanded (S = D). Show your work!!
a.) Find the equilibrium price for hot dogs at the baseball game.
What is the equilibrium quantity?
Equilibrium price = __________ Equilibrium quantity =
_______
2. (See 4.1 # 46) Suppose that a company has just purchased a
new machine for its manufacturing facility for
$120,000. The company chooses to depreciate the machine
using the straight-line method over 10 years.
a.) Write a linear function that expresses the book value of the
machine as a function of its age.
b.) What is the book value of the machine after 4 years?
c.) When will the machine be worth $60,000? Show your
algebra
3. Consider the function
2
_______
2. (See 4.1 # 46) Suppose that a company has just purchased a
new machine for its manufacturing facility for
$120,000. The company chooses to depreciate the machine
using the straight-line method over 10 years.
a.) Write a linear function that expresses the book value of the
machine as a function of its age.
b.) What is the book value of the machine after 4 years?
c.) When will the machine be worth $60,000? Show your
algebra
3. Consider the function
2
Using the completing the square technique, write f(x)
in the form
2
What is the vertex?
What is the axis of symmetry?
Using algebra show your work to find the x intercepts.
(ie. where f(x) =0.)
What is the y-intercept. (i.e. f(0)).
Graph the function.
in the form
2
What is the vertex?
What is the axis of symmetry?
Using algebra show your work to find the x intercepts.
(ie. where f(x) =0.)
What is the y-intercept. (i.e. f(0)).
Graph the function.
4. (4.3 # 36) Consider the function
2
What is the vertex? You may use
2
b
x
a
What is the axis of symmetry?
Using algebra show your work to find the x intercepts.
What is the y-intercept.
2
What is the vertex? You may use
2
b
x
a
What is the axis of symmetry?
Using algebra show your work to find the x intercepts.
What is the y-intercept.
Give intervals where the function is increasing and
decreasing.
Graph the function.
5. (4.3 # 50) Determine the quadratic function for a parabola
that has a vertex at (2, 3) and a y-intercept of
(0, -1). Show the algebra to come up with the leading
coefficient. Leave your answer in the form
2
6. (4.3 # 90) The marginal cost C (in dollars) of manufacturing
x cell phones (in thousands) is given by
2
manufactured to minimize the marginal cost?
decreasing.
Graph the function.
5. (4.3 # 50) Determine the quadratic function for a parabola
that has a vertex at (2, 3) and a y-intercept of
(0, -1). Show the algebra to come up with the leading
coefficient. Leave your answer in the form
2
6. (4.3 # 90) The marginal cost C (in dollars) of manufacturing
x cell phones (in thousands) is given by
2
manufactured to minimize the marginal cost?
What is the minimum marginal cost? Show your algebra. (You
can use
2
b
x
a
7. (4.3 # 92) The daily revenue R achieved by selling x boxes
of candy is modeled by
2
( ) 9.5
The daily cost C of selling x boxes of candy is ( ) 1.25 250C x
a.) How many boxes of candy must the firm sell to maximize
revenue? What is that maximum revenue?
Show algebra.
b.) Profit is given as P(x) = R(x) – C(x). What is the profit
function?
d.) How many boxes of candy must the firm sell to maximize
profit? What is the maximum profit? Show
can use
2
b
x
a
7. (4.3 # 92) The daily revenue R achieved by selling x boxes
of candy is modeled by
2
( ) 9.5
The daily cost C of selling x boxes of candy is ( ) 1.25 250C x
a.) How many boxes of candy must the firm sell to maximize
revenue? What is that maximum revenue?
Show algebra.
b.) Profit is given as P(x) = R(x) – C(x). What is the profit
function?
d.) How many boxes of candy must the firm sell to maximize
profit? What is the maximum profit? Show
your algebra.
8. Use the figure to answer the following question.
a.) Solve f(x) = 0
b.) Solve g(x) < 0
c.) Solve f(x) > g(x)
d.) Solve g(x) = 9
8. Use the figure to answer the following question.
a.) Solve f(x) = 0
b.) Solve g(x) < 0
c.) Solve f(x) > g(x)
d.) Solve g(x) = 9
9. (4.3 # 88) The John Deere Company has found that the
revenue, in dollars from sales of riding mowers is a
function of the unit price p, in dollars, that it charges. If the
revenue R is
21
( ) 1900
2
a.) What unit price should be charge to maximize revenue?
Show your algebra.
b.) What is the maximum revenue?
f(x) g(x)
(1,6)
(0,9)
(0,4)
(3,0)
revenue, in dollars from sales of riding mowers is a
function of the unit price p, in dollars, that it charges. If the
revenue R is
21
( ) 1900
2
a.) What unit price should be charge to maximize revenue?
Show your algebra.
b.) What is the maximum revenue?
f(x) g(x)
(1,6)
(0,9)
(0,4)
(3,0)
MA 116 Turn-in Practice Problems 3.5
Pitts Name ___________________________
1. Look at the graphs in 3.5 # 1 – 14. Give the equation of the
following ones:
a.) # 8 b.) # 10
2. Write the function whose graph is the graph of y = x3, but
is:
a.) # 20: Shifted to the left 4 units. b.) #22: Shifted down
4 units
c.) # 24: Reflected about the x-axis. d.) # 26: Horizontally
stretched by a factor of 4.
3. Find the function that is finally graphed after the following
transformation are applied to the
a.) (# 28) that is reflected about the x-axis, shifted right 3 units
and shifted down 2 units.
Pitts Name ___________________________
1. Look at the graphs in 3.5 # 1 – 14. Give the equation of the
following ones:
a.) # 8 b.) # 10
2. Write the function whose graph is the graph of y = x3, but
is:
a.) # 20: Shifted to the left 4 units. b.) #22: Shifted down
4 units
c.) # 24: Reflected about the x-axis. d.) # 26: Horizontally
stretched by a factor of 4.
3. Find the function that is finally graphed after the following
transformation are applied to the
a.) (# 28) that is reflected about the x-axis, shifted right 3 units
and shifted down 2 units.
Y = _____________________________________
b.) (# 30) shift up 2 units, reflect about the y-axis, and shift
left 3 units.
Y = ___________________________________
4. (# 32) If (3, 6) is a point on the graph of y = f(x), what
point is on the graph of y = f(-x)?
5. (# 34.) If (4, 2) is a point on the graph of y = f(x), which
point is on the graph of y = f(2x)?
6. Graph each of the following, Make sure to clearly show
three key points and give their
coordinates.
a.) # 46
3
( ) ( 2
b.) (# 30) shift up 2 units, reflect about the y-axis, and shift
left 3 units.
Y = ___________________________________
4. (# 32) If (3, 6) is a point on the graph of y = f(x), what
point is on the graph of y = f(-x)?
5. (# 34.) If (4, 2) is a point on the graph of y = f(x), which
point is on the graph of y = f(2x)?
6. Graph each of the following, Make sure to clearly show
three key points and give their
coordinates.
a.) # 46
3
( ) ( 2
7. (See the graph in 3.5 # 69). Suppose y = f(x) is the graph in
the text. Graph the function
-
4, -2), (0, 2), (2,2) and (4, 0) are moved.
f points H points
(-4, -2)
(0, 2)
(2, 2)
(4, 0 )
Using interval notation give the domain
and range of H(x)
Domain ________________
range _________________
Explain in words what is happening.
(i.e. what kinds of shifting, stretching or
the text. Graph the function
-
4, -2), (0, 2), (2,2) and (4, 0) are moved.
f points H points
(-4, -2)
(0, 2)
(2, 2)
(4, 0 )
Using interval notation give the domain
and range of H(x)
Domain ________________
range _________________
Explain in words what is happening.
(i.e. what kinds of shifting, stretching or
shrinking and reflections are occurring.)
8. (See the graph in # 70). Suppose y = f(x) is the graph in the
text. Graph the function
( ) 2 1
2
x
H x f
, showing clearly where (-4, -2),(-2, -2), (2,2) and (4, -2) are
moved.
F points H points
(-4, -2)
(-2, -2)
(2, 2)
8. (See the graph in # 70). Suppose y = f(x) is the graph in the
text. Graph the function
( ) 2 1
2
x
H x f
, showing clearly where (-4, -2),(-2, -2), (2,2) and (4, -2) are
moved.
F points H points
(-4, -2)
(-2, -2)
(2, 2)
(4, -2)
Using interval notation give the domain
and range of H(x)
Domain ________________
range _________________
Explain in words what is happening.
(i.e. what kinds of shifting, stretching or
shrinking and reflections are occurring.)
MA 116 Turn in Practice Problems 3.4
Pitts Name _____________________________
1. (#26) If
Using interval notation give the domain
and range of H(x)
Domain ________________
range _________________
Explain in words what is happening.
(i.e. what kinds of shifting, stretching or
shrinking and reflections are occurring.)
MA 116 Turn in Practice Problems 3.4
Pitts Name _____________________________
1. (#26) If
2
-3x if x < -1
( ) 0 if x = -1
2x +1 if x >-1
f x
. Find the following:
a.) f(-2) b.) f(-1) c.) f(0)
2. Graph the following. Indicate carefully the open and closed
circles. Also give coordiates of key
points. Give the domain and range in interval notation.
a.) # 32)
3 if x < -2
( )
-2x - 3 if x -2
x
-3x if x < -1
( ) 0 if x = -1
2x +1 if x >-1
f x
. Find the following:
a.) f(-2) b.) f(-1) c.) f(0)
2. Graph the following. Indicate carefully the open and closed
circles. Also give coordiates of key
points. Give the domain and range in interval notation.
a.) # 32)
3 if x < -2
( )
-2x - 3 if x -2
x
f x
b.) # 34.)
2 5 if -3 x<0
( ) 3 if x = 0
5 if x > 0
x
f x
x
Domain: __________________ Domain _________________
Range: ___________________ Range
___________________
3. Write the definition for the piecewise-defined function given
in the picture in the text. Also give
b.) # 34.)
2 5 if -3 x<0
( ) 3 if x = 0
5 if x > 0
x
f x
x
Domain: __________________ Domain _________________
Range: ___________________ Range
___________________
3. Write the definition for the piecewise-defined function given
in the picture in the text. Also give
the domain and range.
a.) # 42
( )f x
domain: ____________ range ____________
b.) (# 44)
( )f x
domain ____________ range ____________
MA 116 Turn-in Practice Problems (5.1 & 5.6)
Pitts
a.) # 42
( )f x
domain: ____________ range ____________
b.) (# 44)
( )f x
domain ____________ range ____________
MA 116 Turn-in Practice Problems (5.1 & 5.6)
Pitts
Name __________________________
Give the x-intercepts, give the multiplicity, and tell whether the
curve touches or crosses at each.
Zero multiplicity touches or crosses
What is the degree? ________________ Determine the end
behavior: ________________________
2. (5.1 # 54)
3
2
)1(
3
1
Give the x-intercepts, give the multiplicity, and tell whether the
curve touches or crosses at each.
Zero multiplicity touches or crosses
What is the degree? ________________ Determine the end
behavior: ________________________
2. (5.1 # 54)
3
2
)1(
3
1
Give the x-intercepts, give the multiplicity, and tell whether the
curve touches or crosses at each.
Zero multiplicity touches or crosses
What is the degree? ________________ Determine the end
behavior: ________________________
3. Construct a polynomial function of degree 4 that has x-
intercepts (zeroes) at -1, 1, and 2, crosses at x = -1 and
x = 2, and touches at x = 1 and has has a y-intercept at (0, 4).
You may leave it in factored form, but make
sure you find the correct leading coefficient. Show your
algebra!
f(x) = ______________________________________
4. Factor
5 4 3 2
by grouping or use your calculator.
curve touches or crosses at each.
Zero multiplicity touches or crosses
What is the degree? ________________ Determine the end
behavior: ________________________
3. Construct a polynomial function of degree 4 that has x-
intercepts (zeroes) at -1, 1, and 2, crosses at x = -1 and
x = 2, and touches at x = 1 and has has a y-intercept at (0, 4).
You may leave it in factored form, but make
sure you find the correct leading coefficient. Show your
algebra!
f(x) = ______________________________________
4. Factor
5 4 3 2
by grouping or use your calculator.
5. Use your calculator and what you know about polynomials to
factor:
3 2
6. (5.6 # 24) Solve
3 2
Leave your answer in interval
notation.
Answer in interval notation: ______________________
7. (5.6 # 28) Solve the following inequality
3 2
leave
your answer in interval notation.
Answer in interval notation:
_______________________________
factor:
3 2
6. (5.6 # 24) Solve
3 2
Leave your answer in interval
notation.
Answer in interval notation: ______________________
7. (5.6 # 28) Solve the following inequality
3 2
leave
your answer in interval notation.
Answer in interval notation:
_______________________________
8. (5.6 # 34) Solve the inequality showing your sign graph.
( 3)
0
1
x
x
. Leave your answer in interval
notation.
Answer in interval notation: _____________________________
9. (5.6 # 38). Solve the inequality showing your sign graph.
2
2
( 5)
0
4
x
( 3)
0
1
x
x
. Leave your answer in interval
notation.
Answer in interval notation: _____________________________
9. (5.6 # 38). Solve the inequality showing your sign graph.
2
2
( 5)
0
4
x
x
. Leave your answer in interval
notation.
Answer in interval notation: _____________________________
10. (5.6 # 44) Solve the following inequality
5 3
3 1x x
. Show your algebra. Show your sign graph, and leave
your answer in interval notation. Warning: don’t cross
multiply! I won’t give this hint on the test.
. Leave your answer in interval
notation.
Answer in interval notation: _____________________________
10. (5.6 # 44) Solve the following inequality
5 3
3 1x x
. Show your algebra. Show your sign graph, and leave
your answer in interval notation. Warning: don’t cross
multiply! I won’t give this hint on the test.
Answer in interval notation: _____________________________
11. (5.6 # 58) Solve the following inequality
12
7x
x
. Show your algebra. Show your sign graph, and
leave your answer in interval notation. Warning: don’t multiply
both sides by x!!!
Answer in interval notation: _____________________________
12. Find the domain of
2
25
( )
4
x
11. (5.6 # 58) Solve the following inequality
12
7x
x
. Show your algebra. Show your sign graph, and
leave your answer in interval notation. Warning: don’t multiply
both sides by x!!!
Answer in interval notation: _____________________________
12. Find the domain of
2
25
( )
4
x
f x
x
. Show your work, including your sign graph. Leave your
answer
in interval notation.
Answer in interval notation: _____________________________
x
. Show your work, including your sign graph. Leave your
answer
in interval notation.
Answer in interval notation: _____________________________
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